Our strategy to tackle the problem of uniqueness for poorly regular coefficients of Equation (REF ) may be summerize as follow, and is inpired by the work of Davie [1]}. In order to compensate the lack of Girsanov transform in this setting, we rely on a flow transformation presented in the rough path setting in [2]}. Indeed, it allows us to consider the regularization properties of the flow of the driftless equation. Furthermore, in order to replace the Kolmogorov equations arrising in a Brownian context, we will use some Malliavin calculus in a Gaussian rough path setting, which have been developped by several authors [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}
